Esposito A (2019)
Publication Language: English
Publication Type: Thesis
Publication year: 2019
This PhD thesis is devoted to some mathematical models describing aggregation-diffusion phenomena for two interacting species in several scientific contexts such as, for instance, biology, physics and finance. More precisely, we deal with two types of such models. First, we consider a class of systems of partial differential equations with nonlinear degenerate cross-diffusion and nonlocal interactions, where the former is modelled by a nonlinear function depending on both species, while the latter consists of convolution terms. Then, we focus on a system of continuity equations driven by Newtonion nonlocal interactions in one spatial dimension. The different structure of the previous systems requires a deep analysis in order to provide a systematic mathematical theory leading to their well-posedness as well as some properties of the solutions. These issues will be tackled in the following, by exploiting the theory of gradient flows in Hilbert spaces, and probability spaces, combined with optimal transport techniques.
APA:
Esposito, A. (2019). Systems of PDEs modelling aggregation-diffusion phenomena with many species (Dissertation).
MLA:
Esposito, Antonio. Systems of PDEs modelling aggregation-diffusion phenomena with many species. Dissertation, 2019.
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